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Signals and Systems by Smarajit Ghosh

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6.13 z-TRANSFORM OF CAUSAL COSINE SEQUENCE

The causal cosine sequence is given by

 

x(n) = cos () u(n)

 

Using Euler’s identity, we can write cos (nω) as follow:

 

image

 

The z-transform of above equation is given below.

 

image

 

Let us put α = ejω and β = ejω in the above expression, we get

 

image

we know that    image

 

 

Substituting the individual ...

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